Competition between magnetism and superconductivity in the organic metal kappa-[BEDT-TTF]₂Cu[N(CN)₂]Br

Ultrasonic velocity and attenuation measurements on the quasi-two-dimensional organic conductor $\kappa$-[BEDT-TTF]$_2$Cu[N(CN)$_2$]Br give the first determination of the coexistence zone of the antiferromagnetic and superconducting phases which extends deep in the metallic part of the pressure-temperature phase diagram of these salts. This zone is identified from a precise control of the ordering in ethylene end groups which acts as an internal pressure. The two phases are found to compete whereas superconducting fluctuations begin to contribute to the attenuation at 15 K, namely at the onset of magnetic order that is well above the superconducting transition temperature $T_c$ = 11.9 K. Finally, the temperature profile of sound attenuation for both longitudinal and transverse phonon polarizations is found to be inconsistent with a conventional \textit{s}-wave order parameter.